Null controllability properties of some degenerate parabolic equations.

◮ α ≥ 2 : well-posed with the Neumann boundary condition
(x α u x )(0, t) = 0 = u(1, t), and not null controllable ;
Main tools : application of a result of Escauriaza, Seregin,
Sverak (2004) related to the backward uniqueness properties
of the heat equation in half space.
Remark : Strong connection between degenerate problems in
bounded domains and nondegenerate problems in unbounded
domains
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